Adsorption of ⁸⁵Kr radioactive inert gas into hardening mixtures

Abstract

Changes in volumetric activity of ⁸⁵Kr radioactive inert gas take place in the atmosphere: it has increased by around 50% during the past 15 years. The main source of such gas is the operation of nuclear power plants and spent nuclear fuel reprocessing plants. ⁸⁵Kr as an inert gas spreads throughout the entire atmosphere and its ionizing radiation may result in changes of atmospheric electric phenomena. Therefore it is necessary to control ⁸⁵Kr emission into the atmosphere. However, there is no effective method for this as inert gases, under normal conditions, can hardly be adsorbed in different adsorbents and stored in special containers for a long period of time. This paper tries to show the possibility of keeping ⁸⁵Kr longer within the adsorbent by changing its aggregate state: gas is adsorbed into liquid adsorbent and desorption takes place from solid adsorbent. For this purpose, an epoxy resin is used which, after adding a special hardener at room temperature, turns into a solid material with density of around 1.2 × 10³ kg m⁻³. As a result of sample blending with substances which contribute to better solubility of ⁸⁵Kr, diffusion coefficient of this gas (i.e. desorption speed) changes within the adsorbent in the solid state.

Introduction

As nuclear power expands, radioactive inert gases enter the atmosphere. Long-lived radioactive inert gases take part in the atmospheric circulation system and spread throughout the entire atmosphere. One of the long-lived radioactive inert gases of high importance is Krypton-85 (${}_{36}^{85} {\text{Kr}}$). The radioactivity decay half-life of this radionuclide is T _1/2 = 10.76 m; radioactivity decay constant is λ = 2.04 × 10 ⁻⁹ s⁻¹; 99.563% of radiation consists of beta particles with energy of 0.687 MeV, and the rest of 0.437% of radiation −0.173 MeV. Gamma radiation energy is equal to 0.514 MeV [1, 2].

One of the sources of ⁸⁵Kr in the atmosphere is nuclear explosions and not only in the atmosphere but also under the earth, or under water. A 1 Mt nuclear explosion results in the fission of around 56 kilograms of ²³⁵U; this means 4.6 × 10²³ of ⁸⁵Kr atoms released (0.32% yield) [3]. Supposedly, emissions of ⁸⁵Kr from this source amounted to 111–185 PBq in the atmosphere in 1973 [4]. Atmospheric activity of 5 × 10⁶ Ci caused by ⁸⁵Kr during the period 1945–1962 is indicated in the article Krypton-85 [1].

The other way ⁸⁵Kr gets into the atmosphere is during the operation of nuclear plants; in cases where ²³⁵U fuel is used, activity of this gas amounts to 6.2 × 10¹² Bq (MW m)⁻¹, ²³³U—$12.2 \times 10^{12}\; {\text{Bq}}\;({\text{MW}}\;{\text{m}})^{ - 1}$, ²³⁹Pu—$2.7 \times 10^{13} \;{\text{Bq}}\;({\text{MW}}\;{\text{m}})^{ - 1}$ [3]. Large volumes of ⁸⁵Kr have been released into the atmosphere during accidents in nuclear power plants; e.g. Chernobyl Nuclear Plant catastrophe resulted in emissions of ⁸⁵Kr with activity of around 35 PBq [1, 4], and the Three Mille accident—around $5 \times 10^{4} \;{\text{Ci}}\;(185 \times 10^{13} \;{\text{Bq}})$ [1].

The significant source of atmospheric emissions of ⁸⁵Kr is spent nuclear fuel reprocessing (regeneration) plants; capacity of the activity of ⁸⁵Kr emitted by large plants might amount to $1.8 \times 10^{9} \;{\text{Bq}}\;{\text{s}}^{ - 1}$ [2, 3]. Winger et al. [4] provided detailed evaluation of ⁸⁵Kr emissions from spent nuclear fuel reprocessing plants in La Hague (France), Chelyabinsk (Russia), Tomsk (Russia), Sellafield (UK), Dounray (UK), and Hanford (USA). The above mentioned authors have estimated that activity of ⁸⁵Kr emitted into the atmosphere during the period 1945–2000 reaches up to $10.6 \times 10^{18} \;{\text{Bq}}$ [4]. The paper of Smith et al. [5] determines significant increase of ⁸⁵Kr activity at the sampling location which was in downwind direction from La Hague nuclear fuel reprocessing plant. Most of the authors’ papers [1, 4–7] declare continuous increase of ⁸⁵Kr activity concentration in the atmosphere. Dubasov and Okunev [8] had been monitoring ⁸⁵Kr activity concentration in Cherepovets district (Vologda region) and determined that activity concentration (volumetric activity) of this radionuclide had increased almost by 50% during 15 years and grew from 1.41 to 1.94 Bq m⁻³ during the period 2006–2008. This results correspond to the data of Japanese researchers [9]. As in the past, nowadays, scientists pay much of their attention to modelling the spread of ⁸⁵Kr in the atmosphere as this helps not only to research the distribution of this gas in the atmosphere of the Earth, but also provides information on air mass movement [4, 10–12].

Accumulation of ⁸⁵Kr in the atmosphere intensifies the process of ionization and this might result in irreversible climate changes. Increase of ionization in the atmosphere due to the impact of ionizing radiation of ⁸⁵Kr is shown in the paper by Loosli [13] and proven in the article by Harrison and ApSimon [14]. Possible increase of lightweight ion concentration until 2015 had been researched in the work by Styra and Butkus [3]. Modelling experiments have determined the dependence of lightweight ion concentration increase under conditions of ⁸⁵Kr gas being in contaminated environment [15–18]. Atmospheric ionization may influence geophysical processes most significantly in the atmosphere above the Earth’s surface up to thunderclouds and inside of them. Beta radiation of average energy (0.251 MeV), along the travel distance of 0.751 m, creates 6,459 ion couples in the atmosphere. Increase of ion concentration in the atmosphere results in change of aerosol particle concentration and spectrum. The question whether such processes are capable of changing electrical resistance of the atmosphere and all the atmospheric processes related to it cannot be answered yet.

The other atmospheric phenomena resulted by ionizing radiation of ⁸⁵Kr is the ionization effects inside the thunderclouds. Only the ⁸⁵Kr, being long-lived radionuclide and inactive in reactions with environmental objects, is able to achieve the same volumetric activity inside a thundercloud as on the Earth’s surface [2]. Distribution of radionuclides in the atmosphere provides with information on the flow of air masse [19].

For the purpose of finding out possible impact of ionizing radiation of ⁸⁵Kr to the atmospheric processes, it is necessary to develop modelling experiments in that direction and compare the results with feasible natural observations. We see the necessity of the following experiments and theoretic researches:

• 1. Containment of ⁸⁵Kr to prevent its emissions into the atmosphere from nuclear power plants and nuclear fuel reprocessing companies.

• 2. Development of radioactive inert gas chemistry with the purpose of finding substances in which ⁸⁵Kr could be adsorbed or chemically combined and then disposed in radioactive material containers for a long time.

• 3. Experimental research of the environmental ionization caused by ionizing radiation of ⁸⁵Kr.

• 4. Development of theoretic researches of the above mentioned processes.

Adsorption of ⁸⁵Kr in various substances was actively researched around the middle of the twentieth century [2]. Most of the works of this nature were done using activated charcoal as an adsorbent [20]. However, effective adsorption of inert gases and long time storage in the activated charcoal or other adsorbents is only possible at low temperatures [16].

We have to admit that search for new adsorbents for ⁸⁵Kr is negligible during current period; in fact, some research results have not only scientific but also practical significance [21]. Sorption capacity of radioactive materials varies with an adsorbent pH, time of material contact with an adsorbat [22, 23] and physical status of an adsorbent [24]. However, data to characterize adsorption of ⁸⁵Kr was not found.

The objective of this work is to increase desorption duration and extend the period of gas storage in adsorbents by means of adsorption of long-lived radioactive inert gases into hardening mixtures.

Experimental

For the purpose to achieve the objective of the work, the modelling experiment has been carried out; it started on April 23, 1999. Samples (adsorbents) of six types have been prepared:

Sample 1. E-6 epoxy resin and a hardener; ratio 1:0.1. Sample volume $V = 122 \times 10^{ - 6} \;{\text{m}}^{3}$ (a cylinder with diameter of $d = 72 \times 10^{ - 3} \;{\text{m}}$ and a height of $h = 3 \times 10^{ - 2} \;{\text{m}}$).

Sample 2. E-6 epoxy resin, hardener and toluene; ratio 1:0.1:0.15. Sample volume $163 \times 10^{ - 6} \;{\text{m}}^{3}$ (a cylinder with diameter of $d = 72 \times 10^{ - 3} \;{\text{m}}$ and a height of $h = 4 \times 10^{ - 2} \;{\text{m}}$).

Sample 3. E-6 epoxy resin, hardener and type BAU activated charcoal; ratio 1:0.1:0.5. Sample volume $V = 324 \times 10^{ - 6} \;{\text{m}}^{3}$ (a cylinder with diameter of $d = 72 \times 10^{ - 3} \;{\text{m}}$ and a height of $h = 55 \times 10^{ - 3} \;{\text{m}}$).

Sample 4. E-6 epoxy resin, hardener and type BAU activated charcoal; ratio 1:0.1:0.35. Sample volume $V = 10^{ - 4} \;{\text{m}}^{3}$ (a cylinder with diameter of $d = 72 \times 10^{ - 3} \;{\text{m}}$ and a height of $h = 24,6 \times 10^{ - 3} \;{\text{m}}$).

Sample 5. E-6 epoxy resin, hardener and xylene (grade A oil xylene); ratio 1:0.1:0.35. 0.1:0.13. Sample volume $V = 122 \times 10^{ - 6} \;{\text{m}}^{3}$ (a cylinder with diameter of $d = 72 \times 10^{ - 3} \;{\text{m}}$ and a height of $h = 3 \times 10^{ - 2} \;{\text{m}}$).

Sample 6. E-6 epoxy resin, hardener and butanol (${\text{C}}_{4} {\text{H}}_{9} {\text{OH}}$); ratio 1:0.1:0.13. Sample volume $V = 122 \times 10^{ - 6} \;{\text{m}}^{3}$ (a cylinder with diameter of $d = 72 \times 10^{ - 3} \;{\text{m}}$ and a height of $h = 3 \times 10^{ - 2} \;{\text{m}}$).

During the experiments, temperature of samples has been increasing, especially with type BAU activated charcoal. In this case, volume and temperature of the solid has been increasing rapidly and even broke the closed glass container. There was almost no temperature increase in mixture of epoxy resin and xylene.

The experiment was engineered in the following way. In the “hot zone”, a glass container with volume of $0.5 \times 10^{ - 3} \;{\text{m}}^{3}$ was filled with ⁸⁵Kr gas and sealed. The activity of ⁸⁵Kr gas contained in the vessel has been measured and amounted to $2.75 \times 10^{6} \;{\text{Bq}}$. Gas with such activity was dosed into the container (1) of the experimental system shown in Fig. 1.

Fig. 1

Layout of experimental equipment: 1—⁸⁵Kr dosing container; 2—glass container with hardening mixture; 3—filter; 4—SBT-11 counter for ⁸⁵Kr activity measurement; 5—reometer; 6—column submersed into a liquid nitrogen for adsorption of ⁸⁵Kr contained in the system (system cleaning of ⁸⁵Kr); 7—pump; 8—valve for pressurizing containers (1) and (2); 9—3-way valve for dosing system diversion; 10—hoses to/from ⁸⁵Kr source camera; 11—fume cupboard

Using radioactive gas with known activity value, the effectiveness of the counter 4 (Fig. 1) has been determined and amounted to $K_{1} = 0.79 \times 10^{ - 3} \;{\text{imp}}\;{\text{Bq}}^{ - 1} \;{\text{s}}^{ - 1}$ for ⁸⁵Kr gas. It was used for determination of volumetric activity of ⁸⁵Kr in the system shown in Fig. 1.

While the mixture in the container (2) (Fig. 1) is not hardened, the bubbling method is used to saturate the sample with ⁸⁵Kr gas. A sample is taken for determination of volumetric activity of ⁸⁵Kr by means of UMF-1500M low background radiation device. Effectiveness of this device, when measuring in the standard dish of the device, amounts to $K_{2} = 10^{ - 3} \;{\text{imp}}\;{\text{Bq}}^{ - 1} \;{\text{s}}^{ - 1}$. Volume of the mixture used to fill the dish is $V_{1} = 1.96 \times 10^{ - 6} \;{\text{m}}^{3}$. Calculation of measurement results is performed using this formula:

$$ A_{{V_{1} }} = {\frac{{N_{1} }}{{K_{2} \times V_{1} }}}, $$

(1)

where $A_{{V_{1} }}$ is the volumetric activity of ⁸⁵Kr in a sample, Bq m⁻³; N ₁ the sample radiation intensity, imp s⁻¹; K ₂ the effectiveness of the UMF-1500M device, imp Bq⁻¹ s⁻¹; and V ₁ is the volume of the sample measured, m³. Activity of the background radiation equals to 0.22 imp s⁻¹.

After the mixture in container (2) (Fig. 1) hardens, circular suction in the system is stopped, containers (1) and (2) are pressurized and ⁸⁵Kr remaining in the system is sucked into the column (6). After this, container (2) is disconnected from the system, then broken and the activity of the cylinder-shaped sample taken out is measured using SBT-10 counter.

Activity of the radiation emitted from the surface of the solid sample taken out from the container (2) (Fig. 1) was measured by the SBT-10 counter contained within the lead housing, the diagram of which is shown in Fig. 2. At the beginning of each measurement, the background radiation was determined and fluctuated from 55 to 63 imp s⁻¹.

Fig. 2

Diagram of the housing for measurements of activity of ⁸⁵Kr radiation emitted from solid samples: 1—lead housing; 2—SBT-10 counter; 3—sample

⁸⁵Kr is likely distributed evenly within the sample contained in vessel (2) and the volumetric activity of the gas is close to that of air in the system as inert gases form no compounds at normal conditions.

Results and discussion

⁸⁵Kr desorption from samples

Results of measured volumetric activity of ⁸⁵Kr in the system’s (Fig. 1) air are compared with those calculated by the formula (1). Data obtained presented in Table 1.

Table 1 ${}^{85}{\text{Kr}}$ adsorption level in samples

As we can see in the Table 1, accumulation of ⁸⁵Kr radioactive inert gas in respect to environmental ⁸⁵Kr can only be expected in pure E-6 epoxy resin and mixture with xylene.

Hardened samples were stored at room temperature and a proportion of desorpted ⁸⁵Kr was measured at certain intervals using equipment shown in Fig. 2. Results of the analysis presented in Table 2.

Table 2 ${}^{85}{\text{Kr}}$ desorption rate

The most intense desorption takes place during the first 100 days: it amounts to 1.91 × 10⁻⁴ m⁻² s⁻¹ from mixture of E-6 epoxy resin, hardener and toluene, and mixture of E-6 epoxy resin and a hardener. Desorption significantly slows down in 200 days. ⁸⁵Kr desorption rate from mixture of E-6 epoxy resin, hardener and toluene, and mixture of E-6 epoxy resin and a hardener, not taking into account the decay of nuclear isotope, amounts to an average of $1.9 \times 10^{ - 5} \;{\text{m}}^{ - 2} \;{\text{s}}^{ - 1}$ and $2.1 \times 10^{ - 5} \;{\text{m}}^{ - 2} \;{\text{s}}^{ - 1}$ accordingly.

After all samples were stored 3,870 days at room temperature and then cut horizontally, density of the surface activity (Bq m⁻²) of ⁸⁵Kr in the middle layer was significantly higher than the surface layer. This data presented in Table 3.

Table 3 Ratio of ${}^{85}{\text{Kr}}$ surface activity densities

Figure 3 shows change of ⁸⁵Kr activity concentration (%) in Sample 6 from the centre towards the edge depending on the time t (days).

Fig. 3

Change of ${}^{85}{\text{Kr}}$ activity concentrations (%) in Sample 6 depending on the time t (days)

Model of Krypton concentration distribution in a sample

Decrease of concentration of any radioactive substance in a sample is influenced by two interdependent physical phenomena: spread (diffusion) of a substance through the surface of a sample according to the diffusion equation:

$$ {\frac{{\partial C_{1} }}{\partial t}} = D\Updelta C_{1} , $$

and radioactive decay, intensity of which is proportional to the residual volume of a substance or the activity concentration:

$$ {\frac{{\partial C_{2} }}{\partial t}} = - {\frac{\ln 2}{{T_{1/2} }}}C_{2} , $$

where D is the diffusion coefficient, Δ the Laplace operator, T _1/2 the decay half-life, and C ₁, C ₂ is the respective concentrations.

As these phenomena take place simultaneously, total distribution of concentration in a cylinder-shaped sample (R—base radius, H—height) in the polar coordinate system (φ, r, z) might be defined by the following boundary value problem:

$$ {\frac{\partial C}{\partial t}} = D\left( {{\frac{{\partial^{2} C}}{{\partial r^{2} }}} + \frac{1}{r}\;{\frac{\partial C}{\partial r}} + {\frac{{\partial^{2} C}}{{\partial z^{2} }}}} \right) - {\frac{\ln 2}{{T_{1/2} }}}C $$

(2)

$$ C\left| {_{r = R} = C\left| {_{z = 0} } \right. = C\left| {_{z = H} = 0} \right.} \right.. $$

(3)

Due to the axial symmetry of the sample shape, it is assumed that concentration is not dependent on the angle φ. Moreover, it is supposed that activity concentration, at the beginning of the experiment, is the same in each point of a sample:

$$ C\left| {_{t = 0} = C_{0} = {\text{const}}} \right.. $$

(4)

.

Solution of the marginal problem for distribution of activity concentration of Krypton

Traditionally, boundary value problems in mathematical physics are solved by approximate methods; however, in case of a cylinder-shaped sample, the diffusion problem (2)–(3) can be expressed in analytical form using the method of separation of variables [25]:

$$ C(r,z,t) = \sum\limits_{i = 1}^{\infty } {\sum\limits_{j = 1}^{\infty } {a_{i,j} J_{0} \left( {\mu_{j} r/R} \right)\sin \left( {i\pi z/H} \right)} } \exp \left( { - b_{i,j} t} \right), $$

where

$$ a_{i,j} = {\frac{4}{{R^{2} HJ\left( {\mu_{j} } \right)}}}\int\limits_{0}^{H} {\int\limits_{0}^{R} {C_{0} \left( {r,z} \right)J_{0} \left( {\mu_{j} r/R} \right)\sin \left( {i\pi z/H} \right)r{\text{d}}r{\text{d}}z} } $$

(5)

$$ b_{ij} =\, D\left( {\left( {\mu_{j} /R} \right)^{2} + (i\pi /H) + \ln \,2/T_{1/2} } \right), $$

where $C_{0} (r,z)$ is the initial distribution of concentrations; J _k (r) the Bessel functions of order k; and μ _j is the roots of equation J ₀ (μ) = 0.

On the grounds of condition (4), integral (5) could be calculated and the result is:

$$ \begin{aligned} a_{2i - 1,j} = & 8C_{0} /\left( {\pi (2i - 1)\mu_{j} } \right), \\ a_{2i,j} = & 0 \\ \end{aligned} $$

Solution of the problem (2)–(3) might be expressed as a product of two separate series:

$$ \begin{gathered} C(r,z,t) = {\frac{{8C_{0} }}{\pi }}\exp \left( { - t\ln 2/T_{1/2} } \right) \hfill \\ \times \sum\limits_{i = 1}^{\infty } {{\frac{\sin (\pi (2i - 1)z/H}{2i - 1}}\exp \left( { - Dt\left( {\pi (2i - 1)/H} \right)^{2} } \right)} \hfill \\ \times \sum\limits_{j = 1}^{\infty } {{\frac{{J_{0} (\mu_{j} r/R)}}{{\mu_{j} J_{1} (\mu {}_{j})}}}\exp \left( { - Dt\left( {\mu_{j} /R} \right)^{2} } \right)} , \hfill \\ 0 \le r \le R,0 \le z \le H. \hfill \\ \end{gathered} $$

(6)

Calculation of diffusion coefficient

Let’s take Q(t) as an amount of diffused ⁸⁵Kr during time period of (0,t). Then, the result of integration of flow $- D\int_{S} {{\frac{\partial C}{\partial n}}} {\text{d}}s$ according to time is as follows:

$$ \begin{aligned} Q(t) & = \int\limits_{0}^{t} { - D\int\limits_{S} {{\frac{\partial C}{\partial n}}} {\text{d}}s{\text{d}}t = - D\int\limits_{0}^{t} {\int\limits_{V} {\Updelta C} {\text{d}}V{\text{d}}t} } \\ \; = - D\int\limits_{0}^{t} {\int\limits_{0}^{2\pi } {{\text{d}}\varphi } \,\int\limits_{0}^{H} {\int\limits_{0}^{R} {\left( {{\frac{{\partial^{2} C}}{{\partial r^{2} }}} + \frac{1}{r}{\frac{\partial C}{\partial r}} + {\frac{{\partial^{2} C}}{{\partial z^{2} }}}} \right)r{\text{d}}r{\text{d}}z{\text{d}}t,} } } \\ \end{aligned} $$

(7)

where S,V is the sample’s surface area and volume accordingly and Δ is the Laplace operator.

The initial amount of ⁸⁵Kr is $Q_{0} = \pi R^{2} HC_{0}$ so calculation of integrals (7) including (6) results in the following expression of value $Q(t)/Q_{0}$ characterizing the desorption rate:

$$ \begin{gathered} {\frac{Q(t)}{{Q_{0} }}} = 1 - {\frac{32}{{\pi^{2} }}}\exp \left( { - t\ln 2/T_{1/2} } \right) \hfill \\ \times \sum\limits_{i = 1}^{\infty } {{\frac{{\exp \left( { - Dt\left( {\pi (2i - 1)/H} \right)^{2} } \right)}}{{\left( {2i - 1} \right)^{2} }}}} \;\;\sum\limits_{j = 1}^{\infty } {{\frac{{\exp \left( { - Dt\left( {\mu_{j} /R} \right)^{2} } \right)}}{{\mu_{j}^{2} }}}} . \hfill \\ \end{gathered} $$

(8)

Series of the obtained expression converge rapidly enough (not slower than 1/i ² and 1/j ²) therefore, after calculation of the sum of several tens of members, the accuracy achieved is not lower than the accuracy of desorption measurements performed. Least-squares method (i.e. comparison of calculated $Q(t)/Q_{0}$ values having volatile diffusion coefficient with measured $\widetilde{Q}(t_{i} )/Q_{0}$ values) is used to find approximate values of diffusion coefficients of corresponding samples. These values are presented in Table 4 and distribution of measured $\widetilde{Q}(t_{i} )/Q_{0}$ values in respect of curves (8) is shown in Fig. 4.

Table 4 Mean values of diffusion coefficients of ${}^{85}{\text{Kr}}$

Fig. 4

Measurement results and approximation curves of the data (8)

Mean-square error values, calculated using expression

$$ d = {\frac{{\sqrt {\sum\nolimits_{i = 1}^{n} {\left( {Q(t_{i} )/Q_{0} - \widetilde{Q}(t_{i} )/Q_{0} } \right)} } }}{n}}100\% , $$

stay below 2% in all samples (vary from 0.67 to 2%), and this allows us to suppose that the mathematical model used corresponds sufficiently accurately to the process of activity concentration change, and the values of diffusion coefficients calculated might be used for evaluation of adsorption features of various aggregates.

Conclusions

Cylinder shaped, E-6 epoxy resin based adsorbents with additions of hardener, xylene, toluene, butanol, and activated carbon have been made; volume of the cylinders was $1 \times 10^{ - 4} \;{\text{m}}^{3}$ to $3.24 \times 10^{ - 4} \;{\text{m}}^{3}$ and density in solid state amounted to around $1.2 \times 10^{3} \;{\text{kg}}\;{\text{m}}^{ - 3}$.

In different samples, the volumetric activity of ⁸⁵Kr adsorbed into a liquid sample varied from $0.3 \times 10^{9} \;{\text{Bq}}\;{\text{m}}^{ - 3}$ (Sample 3: mixture with charcoal) to $3.8 \times 10^{9} \;{\text{Bq}}\;{\text{m}}^{ - 3}$ (Sample 5: mixture with xylene).

Desorption of ⁸⁵Kr has been registered during 3,461 days, during 697 of which this was performed regularly. During the mentioned period, when desorption of ⁸⁵Kr has been taking place at room temperature, the mean diffusion coefficient was determined in the adsorbent.

Sample 1—$3.77 \times 10^{ - 13} \;{\text{m}}^{ 2} {\text{s}}^{-1}$; Sample 2—$6.67 \times 10^{ - 13} \;{\text{m}}^{2} {\text{s}}^{-1}$; Sample 3—$130.79 \times 10^{ - 13} \;{\text{m}}^{2} {\text{s}}^{-1}$; Sample 4—$14.00 \times 10^{ - 13} \;{\text{m}}^{2} {\text{s}}^{-1}$; Sample 5—$3.55 \times 10^{ - 13} \;{\text{m}}^{2} {\text{s}}^{-1}$; Sample 6—$7.84 \times 10^{ - 13} \;{\text{m}}^{2} {\text{s}}^{-1}$.

As diffusion of ⁸⁵Kr from a sample into the environment takes place, the distribution of ⁸⁵Kr in not continuous in a sample; after 3,870 days, the density of the surface activity of ⁸⁵Kr is higher in outer layers than in the inner ones: Sample 1—by 3.1 times; Sample 2—by 9.3 times; Sample 4—by 7.2 times; Sample 5—by 5.2 times; Sample 6—by 3.8 times.

Adsorption effectiveness and desorption rate of ⁸⁵Kr in a sample depends on sample’s admixtures which contribute to rapid solubility of this gas.